The number of UK house sales rose at the fastest pace for 16 months in September, the Royal Institution of Chartered Surveyors (Rics) has said.
It is the fifth month in a row that sales have increased.
However, Rics added there was an increasing shortage of properties on the market, which was likely to push up prices.
In the South East, the average number of homes on the books of each surveyor fell to a record low of just 25.
Across the UK, the average stock per surveyor remains at 47, the smallest number recorded.
"It is hard not to see prices continuing to move higher over the coming months, and into the early part of 2016, notwithstanding the present concerns regarding the affordability of housing in some areas of the UK," said Rics chief executive Simon Rubinsohn.
On Wednesday, David Cameron promised a "national crusade" to build more houses.
In particular, the government wants developers to build more affordable homes for first-time buyers.
But its starter homes programme has been criticised by housing groups who argue it will mean fewer affordable homes for rent.